PSI - Issue 2_A

Stefan Kolitsch et al. / Procedia Structural Integrity 2 (2016) 3026–3039 Stefan Kolitsch/ Structural Integrity Procedia 00 (2016) 000–000

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9

t = + ⋅ 1 2

α

.

(11)

k

ρ

As it can be seen from Fig. 3, the load ratio has a marked influence on the crack growth rate. In the notched specimens, cyclic plastic deformation at the notch root causes a long-range residual stress field in front of the notch whose extension depends on the notch acuity t/ ρ . This residual stress field influences the local load ratio at the crack tip until the crack has grown beyond its range (the short-range crack tip plastic zone of the standard SE(B) specimens is accounted for already by Eqns 4-8. In the experiments the two different notch types were loaded at a stress ratio R = 0.1 with two different applied stresses. These conditions were simulated by using the Finite Element Method (FEM). It is assumed that the plastic zone is stabilized after 10 cycles. The resulting local stress ratio R as a function of the distance from the notch root is shown in Fig 5. It can be observed that the plastic zone depends on the notch geometry as well as on the externally applied notch root stress range. The local stress ratio starts for all specimens at a negative value at the notch root and changes to a positive value after a certain distance. This varying stress ratio has to be considered when using Eq. 4 for calculating the crack growth.

Fig. 5. Local stress ratio in front of the notch for different geometries and notch stress levels for a global stress ratio R = 0.1

A further complication comes from the behavior of physically short cracks: after the crack has initiated, the crack growth will first follow the curve for R = 0.7 (no crack closure) regardless of the actual applied load ratio. After a certain crack length is reached and the build-up of crack closure is complete, the growth curve will follow the NASGRO equation for long cracks at the actual local load ratio (which is governed by the residual stress field and by the applied load). As mentioned before, a straight crack front is assumed.